$\dfrac{\csc\theta} {\sin^2 \theta + \cos^2 \theta} = \; ?$
Answer: We can use the identity ${\sin^2 \theta} + {\cos^2 \theta} = 1$ to simplify this expression. $1$ ${\sin\theta}$ ${\cos\theta}$ $\theta$ We can see why this is true by using the Pythagorean Theorem. So, $\dfrac{\csc\theta} {\sin^2 \theta + \cos^2 \theta} = \dfrac{\csc\theta}{1} = \csc\theta$